Problem
Research questions and friction points this paper is trying to address.
Integrated Sensing and Communication
Rate-Distortion Trade-off
Dynamic Tracking
Fundamental Limits
Partially Observed Control
Fundamental Limits of Dynamic Tracking and Communication: A Stationary Policy Formulation
🤖 AI Summary
This study addresses the communication and moving target tracking trade-off in multi-antenna integrated sensing and communication (ISAC) systems by formulating it as a rate-distortion optimization problem, utilizing the posterior Cramér-Rao bound (PCRB) to construct the feasible region. Methodologically, it proposes a belief-augmented information state and proves that stationary randomized policies suffice for covariance scalarization. By integrating Verdú-Han information spectra, Kalman filtering, and convex optimization, the work derives a Gaussian covariance control outer bound under large blocklengths and establishes the optimality of Gaussian signaling. Furthermore, an extended Kalman filter-based achievable frontier and a PCRB outer bound are constructed to characterize the performance limits of dynamic ISAC systems. These findings provide rigorous theoretical foundations for joint sensing and communication design.
📝 Abstract
We study a dynamic integrated sensing-and-communication problem in which a multi-antenna transmitter communicates with a receiver while simultaneously tracking a moving target governed by a stable Gauss--Markov model. We formulate the sensing--communication trade-off as a rate--distortion problem, where the communication rate is defined through the Verdú--Han information spectrum and the sensing distortion is measured by the long-run minimum mean square tracking error in angle and distance. We construct a tractable outer region by lower bounding this distortion through the posterior Cramér--Rao bound (PCRB). The control problem is partially observed because the target state is not directly available to the transmitter. We therefore introduce a belief-augmented information state and show, under the stated regularity assumptions, that stationary randomized Markov policies suffice for the covariance-based scalarized problem used in the outer bound. We then derive, under the stated large-block conditions, a Gaussian covariance-control outer bound by showing that, in the large-block regime, the sensing belief transition becomes asymptotically covariance sufficient; consequently, Gaussian signaling with the same stationary covariance policy preserves the stationary PCRB asymptotically while maximizing the communication reward for each transmit covariance. Numerical experiments compare an extended Kalman filter-based achievable frontier with a PCRB-based Gaussian covariance-control outer frontier.
Innovation
Methods, ideas, or system contributions that make the work stand out.
Integrated Sensing and Communication
Rate-Distortion
Posterior Cramér-Rao Bound
Belief-Augmented Information State
Gaussian Covariance Control
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